Solve for $x$ and $y$ using elimination. ${3x-y = 20}$ ${5x-2y = 32}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-6x+2y = -40}$ $5x-2y = 32$ Add the top and bottom equations together. $-x = -8$ $\dfrac{-x}{{-1}} = \dfrac{-8}{{-1}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {3x-y = 20}\thinspace$ to find $y$ ${3}{(8)}{ - y = 20}$ $24-y = 20$ $24{-24} - y = 20{-24}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 8}$ into $\thinspace {5x-2y = 32}\thinspace$ and get the same answer for $y$ : ${5}{(8)}{ - 2y = 32}$ ${y = 4}$